Statistical inference using a weighted difference-based series approach for partially linear regression models

Partially linear regression models with fixed effects are useful tools for making econometric analyses and normalizing microarray data. Baltagi and Li (2002) [7] proposed a computation friendly difference-based series estimation (DSE) for them. We show that the DSE is not asymptotically efficient in most cases and further propose a weighted difference-based series estimation (WDSE). The weights in it do not involve any unknown parameters. The asymptotic properties of the resulting estimators are established for both balanced and unbalanced cases, and it is shown that they achieve a semiparametric efficient boundary. Additionally, we propose a variable selection procedure for identifying significant covariates in the parametric part of the semiparametric fixed-effects regression model. The method is based on a combination of the nonconcave penalization (Fan and Li, 2001 [13]) and weighted difference-based series estimation techniques. The resulting estimators have the oracle property; that is, they can correctly identify the true model as if the true model (the subset of variables with nonvanishing coefficients) were known in advance. Simulation studies are conducted and an application is given to demonstrate the finite sample performance of the proposed procedures.